Porous implant structures

ABSTRACT

Porous biocompatible structures suitable for use as medical implants and methods for fabricating such structures are disclosed. The disclosed structures may be fabricated using rapid manufacturing techniques. The disclosed porous structures each have a plurality of struts and nodes where no more than two struts intersect one another to form a node. Further, the nodes can be straight, curved, and can include portions that are curved and/or straight. The struts and nodes can form cells that can be fused or sintered to at least one other cell to form a continuous reticulated structure for improved strength while providing the porosity needed for tissue and cell in-growth.

CROSS-REFERENCE TO RELATED APPLICATION

The present application is a continuation of U.S. patent applicationSer. No. 17/158,397, filed Jan. 26, 2021, which is a divisional of U.S.patent application Ser. No. 15/603,936, filed May 24, 2017, now issuedas U.S. Pat. No. 10,945,847, which is a divisional of U.S. patentapplication Ser. No. 13/391,126, filed May 2, 2012 and now issued asU.S. Pat. No. 9,668,863, which is a U.S. National Phase of InternationalPCT Application No. PCT/US2010/046032, filed Aug. 19, 2010, which claimsthe benefit of U.S. Provisional Patent Application Ser. No. 61/235,269,filed Aug. 19, 2009, the contents of each application herebyincorporated by reference herein in their entirety.

FIELD OF THE INVENTION

The present invention generally relates to porous structures suitablefor medical implants, and moss particularly to porous structuressuitable for medical implants that have improved combinations ofstrength, porosity and connectivity and methods for fabricating suchimproved porous structures.

BACKGROUND

Metal foam structures are porous, three-dimensional structures with avariety of uses, including medical implants. Metal foam structures aresuitable for medical implants, particularly orthopedic implants, becausethey have the requisite strength for weight bearing purposes as well asthe porosity to encourage bone/tissue in-growth. For example, manyorthopedic implants include porous sections that provide a scaffoldstructure to encourage bone in-growth during healing and a weightbearing section intended to render the patient ambulatory more quickly.

Metal foam structures can be fabricated by a variety of methods, Forexample, one such method Is mixing a powdered metal with a pore-formingagent (PFA) and then pressing the mixture into the desired shape. ThePFA is removed using heal in a “burn out” process. The remaining metalskeleton may then be sintered to form a porous metal foam structure.

Another similar conventional method include applying a binder topolyurethane foam, applying metal powder to the binder, burning out thepolyurethane foam and sintering the metal powder together to form a“green” part. Binder and metal powder are re-applied to the green partand the green part is re-entered until the green part has the desiredstrut thickness and porosity. The green part is then machined to thefinal shape and re-sintered.

While metal foams formed by such conventional methods provide goodporosity, they may not provide sufficient strength to serve as weightbearing structures in many medical implants. Further, the processes usedto form metal foams may lead to the formation of undesirable metalcompounds in the metal foams by the reaction between the metal and thePFA. Conventional metal foam fabrication processes also consumesubstantial amounts of energy and may produce noxious fumes.

Rapid manufacturing technologies (RMT) such as direct metal fabrication(DMF) and solid free-form fabrication (SFF) have recently been used toproduce metal foam used in medical implants or portions of medicalimplants. In general, RMT methods allow for structures to be built from3-D CAD models. For example, DMF techniques produce three-dimensionalstructures one layer at a time from a powder which is solidified byirradiating a layer of the powder with an energy source such as a laseror an electron beam. The powder is fused, melted, or sintered, by theapplication of the energy source, which is directed in raster-scanfashion to selected portions of the powder layer. After fusing a patternin one power layer, an additional layer of powder is dispensed, and theprocess is repeated with fusion taking place between the layers, untilthe desired structure is complete.

Examples of metal powders reportedly used in such direct fabricationtechniques include two-phase metal powders of the copper-tin,copper-solder, and bronze-nickel systems. The metal structures formed byDMF may be relatively dense, for example, having densities of 70% to 80%of a corresponding molded metal structure, or conversely, may berelatively porous, with porosities approaching 80% or more.

While DMF can be used to provide dense structures strong enough to serveas weight bearing structures in medical implants, such structures do nothave enough porosity to promote tissue and bone in-growth. Conversely,DMF can be used to provide porous structures having enough porosity topromote tissue and bone in-growth, but such porous structures lack thestrength needed to serve as weight bearing structures. Other laser RMTtechniques are similarly deficient for orthopedic implants requiringstrength, porosity, and connectivity.

As a result of the deficiencies of metal foam implants and implantsfabricated using conventional DMF methods, some medical implants requiremultiple structures, each designed for one or more different purposes.For example, because some medical implants require both a porousstructure to promote bone and tissue in-growth and a weight bearingstructure, a porous plug may be placed in a recess of a solid structureand the two structures may then be joined by sintering. Obviously, usinga single structure would be preferable to using two distinct structuresand sintering them together.

In light of the above, there is still a need for porous implantstructures that provide both the required strength and desired porosity,particularly for various orthopedic applications. This disclosureprovides improved porous structures that have both the strength suitablefor weight bearing structures and the porosity suitable for tissuein-growth structures and a method for fabricating such improved porousstructures.

SUMMARY OF THE INVENTION

One objective of the invention is to provide porous biocompatiblestructures suitable for use as medical implants that have improvedstrength and porosity.

Another objective of the invention is to provide methods to fabricateporous biocompatible structures suitable for use as medical implantsthat have improved strength and porosity.

To meet the above objectives, there is provided, in accordance with oneaspect of the invention, there is a porous structure comprising: aplurality of struts, each strut comprises a first end, a second end; anda continuous elongated body between the first and second ends, where thebody has a thickness and a length; and a plurality of nodes, each nodecomprises an intersection between one end of a first strut and the bodyof a second strut.

In a preferred embodiment, the first and second ends of one or morestruts extend between the body of two other struts. In another preferredembodiment, the body of one or more struts comprise a plurality ofnodes.

In accordance with another aspect of the invention, there is a porousstructure comprising a plurality of struts, wherein one or more strutscomprise a curved portion having a length and thickness; a plurality ofjunctions where two of said curved portions intersect tangentially; anda plurality of modified nodes, each modified node comprises an openingformed by three or more of said junctions.

In a preferred embodiment, the porous structure includes at least onestrut comprising a straight portion having a length and a thickness. Inanother preferred embodiment, the porous structure includes at least onestrut having a first end, a second end; and a continuous elongated bodybetween the first and second ends, where the body has a thickness and alength; and at least one closed node comprising an intersection betweenone end of a first strut and the body of a second strut, wherein thestrut can comprise of a straight portion, a curved portion, or both.

In accordance with another aspect of the invention, there are methodsfor fabricating a porous structure. One such method comprises the stepsof: creating a model of the porous structure, the creation stepcomprises defining a plurality of struts and a plurality of nodes toform the porous structure and fabricating the porous structure accordingto the model by exposing metallic powder to an energy source. Thedefining step comprises the steps of providing a first end, a secondend; and a continuous elongated body between the first and second endsfor each strut, selecting a thickness a length for the body; andproviding an intersection between one end of a first strut and the bodyof a second strut for each node.

In a preferred embodiment, the method includes defining the first andsecond ends of one or more struts extend between the body of two otherstruts. In another preferred embodiment, defining the body of one ormore struts to comprise a plurality of nodes.

In accordance with another aspect of the invention, a second method forfabricating a porous structure comprises the steps of: creating a modelof the porous structure: the creation step comprises selecting at leastone frame shape and size for one or more cells of the porous structure,where the frame shape comprises a geometric shape selected from thegroup consisting of Archimedean shapes, Platonic shapes, strictly convexpolyhedrons, prisms, anti-prisms and combinations thereof: adding one ormore struts to the frame where the struts comprises a curved portion,said adding step is performed by inscribing or circumscribing the curvedportion of the one or more struts within or around one or more faces ofthe selected shape; selecting a thickness for the frame and the one ormore struts; and fabricating the porous structure according to the modelby exposing metallic powder to an energy source.

In a preferred embodiment, the creation step includes the step ofremoving a portion of the frame from one or more cells of the model. Inanother preferred embodiment, the fabrication step includes definingN_((1, x)) layer-by-layer patterns for the porous structure based on theselected dimensions, at least one cell shape and at least one cell size,where N ranges from 1 for the first layer at a bottom of the porousstructure to x for the top layer at a top of the porous structure;depositing an N^(th) layer of powdered biocompatible material; fusing orsintering the N^(th) pattern in the deposited N^(th) layer of powderedbiocompatible material; and repeating the depositing and fusing orsintering steps for N=1 through N=x.

In a refinement, the method may further comprise creating a model of theporous structure wherein, for at least some nodes, no more than twostruts intersect at the same location.

In another refinement, the method may comprise creating a model of theporous structure wherein at least one strut or strut portion is curved.

The disclosed porous structures may be fabricated using a rapidmanufacturing technologies such as direct metal fabrication process. Thestruts can be sintered, melted, welded, bonded, fused, or otherwiseconnected to another strut. The struts and nodes can define a pluralityof fenestrations. Further, the struts and nodes can be fused, melted,welded, bonded, sintered, or otherwise connected to one another to forma cell, which can be fused, melted, welded, bonded, sintered, orotherwise connected to other cells to form a continuous reticulatedstructure.

In some refinements, at least one, some, or all struts of a cell mayhave a uniform strut diameter. In some refinements, one, some, or all ofthe struts of a cell may have a non-uniform strut diameter. In somerefinements, a cell may have combinations of struts having uniform andnon-uniform strut diameters. In some refinements, at least one, some, orall of the uniform diameter struts of a cell may or may not sharesimilar, different, or identical strut diameters, longitudinal shapes,cross-sectional shapes, sizes, shape profiles, strut thicknesses,material characteristics, strength profiles, or other properties. Insome refinements, one, some, or all struts within a cell may grow orshrink in diameter at similar, different, or identical rates along apredetermined strut length.

In some refinements, struts within a cell may extend between two nodes.In a further refinement of this concept, struts may have varyingcross-sectional diameters along a strut length, including a minimumdiameter at a middle portion disposed between the two nodes. In furtherrefinement of this concept, struts may have two opposing ends, with eachend connected to a node and a middle portion disposed between the twoends. Struts may flare or taper outwardly as they extend from the middleportion towards each node so that a diameter of the middle portion isgenerally smaller than a diameter of either or both of the two opposingends. In some instances, the struts may flare in a parabolic flutedshape or may taper frusto-conically.

In other refinements, at least one, some, or all struts within a cellare curved. In further refinement of this concept, one, some, or all ofthe cells within a porous structure comprise at least one curved strut.In further refinement of this concept, all of the struts that make up aporous structure are curved. In further refinement of this concept,curved struts may form complete rings or ring segments. The rings orring segments may be inter-connected to form open sides or fenestrationsof multiple-sided cells. In some instances, a single ring may form ashared wall portion which connects two adjacent multiple-sided cells. Insome instances, one or more ring segments alone or in combination withstraight strut portions may form a shared wall portion which connectstwo adjacent multiple-sided cells. In still a further refinement, thenumber of sides of each cell may range from about 4 to about 24. Morepreferably, the number of sides of each cell may range from about 4 toabout 16. One geometry that has been found to be particularly effectiveis a dodecahedron or 12 sided cell. However, as explained andillustrated below, the geometries of the individual cells or the cellsof the porous structure may vary widely and, in the geometries, may varyrandomly front cell to cell of a porous structure.

In another refinement, the configurations of the cells, struts, nodesand/or junctions may vary randomly throughout the porous structure tomore closely simulate natural bone tissue.

In another refinement, each cell may be multiple-sided and having anoverall shape that may fit within a geometric shape selected from thegroup consisting of tetrahedrons, truncated tetrahedrons,cuboctahedrons, truncated hexahedrons, truncated octahedrons,rhombicuboctahedrons, truncated cuboctahedrons, snub hexahedrons, snubcuboctahedrons, icosidodecahedrons, truncated dodecahedrons, truncatedicosahedrons, rhombicosidodecahedrons, truncated icosidodecahedrons,snub dodecahedrons, snub icosidodecahedrons, cubes, octahedrons,dodecahedrons, icosahedrons, prisms, prismatoids, antiprisms, uniformprisms, right prisms, parallelepipeds, cuboids, polytopes, honeycombs,square pyramids, pentagonal pyramids, triangular cupolas, squarecupolas, pentagonal cupolas, pentagonal rotundas, elongated triangularpyramids, elongated square pyramids, elongated pentagonal pyramids,gyroelongated square pyramids, gyroelongated pentagonal pyramids,triangular dipyramids, pentagonal dipyramids, elongated triangulardipyramids, elongated square dipyramids, elongated pentagonaldipyramids, gyroelongated square dipyramids, elongated triangularcupolas, elongated square cupolas, elongated pentagonal cupolas,elongated pentagonal rotundas, gyroelongated triangular cupolas,gyroelongated square cupolas, gyroelongated pentagonal cupolas,gyroelongated pentagonal rotundas, gyrobifastigium, triangularorthobicupolas, square orthobicupolas, square gyrobicupolas, pentagonalorthobicupolas, pentagonal gyrobicupolas, pentagonalorthocupolarotundas, pentagonal gyrocupolarotundas, pentagonalorthobirotundas, elongated triangular orthobicupolas, elongatedtriangular gyrobicupolas, elongated square gyrobicupolas, elongatedpentagonal orthobicupolas, elongated pentagonal gyrobicupolas, elongatedpentagonal orthocupolarotundas, elongated pentagonal gyrocupolarotundas,elongated pentagonal orthobirotundas, elongated pentagonalgyrobirotundas, gyroelongated triangular bicupolas, gyroelongated squarebicupolas, gyroelongated pentagonal bicupolas, gyroelongated pentagonalcupolarotundas, gyroelongated pentagonal birotundas, augmentedtriangular prisms, biaugmented triangular prisms, triaugmentedtriangular prisms, augmented pentagonal prisms, biaugmented pentagonalprisms, augmented hexagonal prisms, parabiaugmented hexagonal prisms,metabiaugmented hexagonal prisms, triaugmented hexagonal prisms,augmented dodecahedrons, parabiaugmented dodecahedrons, metabiaugmenteddodecahedrons, triaugmented dodecahedrons, metabidiminishedicosahedrons, tridiminished icosahedrons, augmented tridiminishedicosahedrons, augmented truncated tetrahedrons, augmented truncatedcubes, biaugmented truncated cubes, augmented truncated dodecahedrons,parabiaugmented truncated dodecahedrons, metabiaugmented truncateddodecahedrons, triaugmented truncated dodecahedrons, gyraterhombicosidodecahedrons, parabigyrate rhombicosidodecahedrons,metabigyrate rhombicosidodecahedrons, trigyrate rhombicosidodecahedrons,diminished rhombicosidodecahedrons, paragyrate diminishedrhombicosidodecahedrons, metagyrate diminished rhombicosidodecahedrons,bigyrate diminished rhombicosidodecahedrons, parabidiminishedrhombicosidodecahedrons, metabidiminished rhombicosidodecahedrons,gyrate bidiminished rhombicosidodecahedrons, and tridiminishedrhombicosidodecahedrons, snub disphenoids, snub square antiprisms,sphenocorons, augmented sphenocoronas, sphenomegacoroma,hebesphenomegacorona, disphenocingulum, bilunabirotundas, triangularhebesphenorotundas, and combinations thereof.

In another refinement, the powder is selected from the group consistingof metal, ceramic, metal-ceramic (cermet), glass, glass-ceramic,polymer, composite, and combinations thereof.

In another refinement, the metallic material is selected from the groupconsisting of titanium, titanium alloy, zirconium, zirconium alloy,niobium, niobium alloy, tantalum, tantalum alloy, nickel-chromium (e.g.,stainless steel), cobalt-chromium alloy and combinations thereof.

In another refinement, the porous structure forms at least a portion ofa medical implant, such as an orthopedic implant, dental implant, orvascular implant.

Porous orthopedic implant structures for cell, and tissue in-growth andweight bearing strength are also disclosed that may be fabricated usinga near-net shape manufacturing process such as a direct metalfabrication (DMF) process for use with metallic biomaterials or astereo-lithography manufacturing process for use with polymericbiomaterials. In instances where a DMF process is utilized, a powderedbiocompatible material is provided in layers and individual particles ofone layer of powdered biocompatible material are fused or sinteredtogether one layer at a time. Exemplary porous structures comprise aplurality of three-dimensional cells. Each cell comprises a plurality ofstruts. Each strut may be sintered or fused to one other strut at anode. Each node may comprise a junction of not more than two struts. Thestruts and nodes of each cell define a plurality of fenestrations. Eachcell comprises from about 4 to about 24 fenestrations. At least onestrut of at least some of the cells are curved. Each cell may be fusedor sintered to at least one other cell to form a continuous reticulatedstructure.

Other advantages and features will be apparent from the followingdetailed description when read in conjunction with the attacheddrawings. The foregoing has outlined rather broadly the features andtechnical advantages of the present invention in order that the detaileddescription of the invention that follows may be better understood.Additional features and advantages of the invention will be describedhereinafter which form the subject of the claims of the invention. Itshould be appreciated by those skilled in the art that the conceptionand specific embodiment disclosed may be readily utilized as a basis formodifying or designing other structures for carrying out the samepurposes of the present invention. It should also be realized by thoseskilled in the art that such equivalent constructions do not depart fromthe spirit and scope of the invention as set forth in the appendedclaims. The novel features which are believed to be characteristic ofthe invention, both as to its organization and method of operation,together with further objects and advantages will be better understoodfrom the following description when considered in connection with theaccompanying figures. It is to be expressly understood, however, thateach of the figures is provided for the purpose of illustration anddescription only and is not intended as a definition of the limits ofthe present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention reference isnow made to the following descriptions taken in conjunction with theaccompanying drawing, in which:

FIGS. 1A-1B illustrate 3-D representations of an example of the strutsat a node in a porous structure of the prior art where the struts ofFIG. 1A have like diameters and the struts of FIG. 1B have differentdiameters.

FIG. 2 is a SEM (Scanning Electron Microscope) microphotograph of anexample of fractured struts of the prior art.

FIGS. 3-5 illustrate 3-D representations of one embodiment of the strutsand nodes of the present invention.

FIGS. 6-8 illustrate 3-D representations of another embodiment of thestruts and nodes of the present invention where at least some of thestruts comprises a smaller cross-sectional diameter at the body portionof the strut as compared to the cross-sectional diameter at the node.

FIGS. 9A and 9B illustrate plan views of the embodiments in FIGS. 6-8 .

FIGS. 10A-10F illustrate 2-D representations of various configurationsof the frame of struts and nodes in a porous structure of the prior art.

FIGS. 11A-11F illustrate 2-D representations of the correspondingconfigurations of the frame of struts and nodes of the prior art inFIGS. 10A-10F modified by one embodiment of the present invention.

FIGS. 12A-12D illustrate 3-D representations of exemplary embodiments ofthe porous structure of the present invention comprising one or moreframe configurations in FIGS. 11A-11F.

FIGS. 13A-13M illustrate 2-D representations of various exemplaryconfigurations of the frame of the two struts of the present inventionforming a node, including frames for struts that are straight curved, ora combination of both.

FIG. 14 illustrates a 2-D representation of an exemplary embodiment ofthe porous structure of the present invention comprising one or moreframe configurations in FIGS. 13A-13M.

FIGS. 15A-15C illustrate 2-D representations of exemplary configurationsof various curved frames and corresponding struts of the presentinvention intersecting to form a node.

FIG. 16 illustrates a 3-D representation of an exemplary embodiment ofthe porous structure of the present invention comprising one or moreframe configurations in FIGS. 13A-13M, including frames for struts thatare straight, curved, or a combination of both.

FIG. 17 illustrates a 3-D representation of an exemplary frame for agenerally cubical cell of the porous structure of the present invention.

FIG. 18 illustrates a 3-D representation of an exemplary arrangement offrames for cubical cells in FIG. 17 .

FIG. 19 illustrates a 3-D representation of an arrangement of cubicalcells of the porous structure of the prior art.

FIG. 20 illustrates a 3-D representation of an exemplary arrangement ofcubical cells of the porous structure of the present invention.

FIG. 21 illustrates a blown up view of the arrangement in FIG. 20 .

FIG. 22 illustrates a 3-D representation of an exemplary frame for atetrahedron-shaped cell of the porous structure of the presentinvention.

FIG. 23 illustrates a 3-D representation of an exemplary frame forsquare-based pyramid cell of the porous structure of the presentinvention.

FIGS. 24A and 24B illustrate various views of 3-D representations of aconventional cell of the porous structure of the prior art based on adodecahedral shape.

FIGS. 25A and 25B illustrate various views of 3-D representations of oneembodiment of a cell of the porous structure of the present inventionalso based on a dodecahedral shape.

FIGS. 26-28 illustrate 3-D representations of a frame of the conventioncell in FIGS. 24A and 24B modified by one embodiment of the presentinvention.

FIGS. 29A and 29B illustrate 3-D representations of a cell of thepresent invention formed from FIGS. 26-28 , where FIG. 29B is a partialview of a 3-D representation of the frame of the cell.

FIG. 30 illustrates the frame of FIG. 27 unfolded into a 2-Drepresentation.

FIG. 31 illustrates a frame of a truncated tetrahedral cell unfoldedinto a 2-D representation.

FIG. 32 illustrates the frame of FIG. 31 formed with curved strutsaccording to one embodiment of the present invention.

FIG. 33 illustrates the frame of a truncated octahedral cell unfoldedinto a 2-D representation.

FIG. 34 illustrates the frame of FIG. 33 formed with curved strutsaccording to one embodiment of the present invention.

FIGS. 35A-35E illustrate 2-D representations of examples of a circle oran ellipse inscribed within various geometric shapes according to oneembodiment of the present invention.

FIG. 36 illustrates the frame of a truncated tetrahedral cell unfoldedinto a 2-D representation with circles circumscribed around each face ofthe cell according to one embodiment of the present invention.

FIGS. 37A and 37B illustrate various views of 3-D representations ofanother embodiment of a cell of the present invention based on adodecahedral shape.

FIG. 38 illustrates a 3-D representation of yet another embodiment of acell of the present invention based on a dodecahedral shape.

FIGS. 39A-39C illustrate various views of 3-D representations of yetanother embodiment of a cell of the present invention based on adodecahedral shape.

FIG. 40 illustrates a 3-D representation of an exemplary arrangement ofthe cells of FIGS. 24 and 25 .

FIGS. 41A and 41B illustrate various views of 3-D representations of anexemplary arrangement of the cells of FIGS. 24, 25, and 37 .

FIG. 42 illustrates a 3-D representation of an exemplary arrangement ofthe cells based on a truncated tetrahedral shape having one or morecurved struts.

FIG. 43 illustrates a 3-D representation of an exemplary arrangement ofthe present invention of cells based on truncated octahedra.

FIG. 44 illustrates a 3-D representation of an exemplary arrangement ofthe present invention of cells based on cubes (light grey), truncatedcuboctahedra (black), and truncated octahedra (dark grey).

FIG. 45 illustrates a 3-D representation of an exemplary arrangement ofthe present invention of cells based on cuboctahedra (black), truncatedoctahedra (dark grey) and truncated tetrahedra (light grey).

FIG. 46 illustrates a flame view of the arrangement of FIG. 42 .

FIG. 47 illustrates a frame view of the arrangement of FIG. 43 .

FIGS. 48-50 illustrate 3-D representations of a frame based onoctahedron modified by one embodiment of the present invention.

FIGS. 51A and 51B illustrate various views of 3-D representations of acell of the present invention formed from the frames of FIGS. 48-50 .

FIG. 52 illustrates a 3-D representation of a frame based a truncatedtetrahedron.

FIGS. 53A-53D Illustrate various views of 3-D representations of a cellformed from the frame of FIG. 52 that was modified by one embodiment ofthe present invention.

FIGS. 54A-54E illustrate various views of 3-D representations of anexemplary arrangement of the cells of FIG. 53 .

FIGS. 55A-55E illustrate 3-D representations of a cell formed from aframe based on a hexagonal prism that was modified by one embodiment ofthe present invention.

FIGS. 56A-56B and 57A-57B illustrate 3-D representations of an exemplaryarrangement of the cells of FIG. 55 .

FIGS. 58-61 illustrate 3-D representations of frames based on adodecahedron modified by various embodiments of the present invention.

It should be understood that the drawings are not necessarily to scaleand that the disclosed embodiments are sometimes illustrateddiagrammatically and in partial views. In certain instances, detailswhich are not necessary for an undemanding of the disclosed methods andapparatuses or which render other details difficult to perceive may havebeen omitted. Also, for simplification purposes, there may be only oneexemplary instance, rather than all, is labeled. It should beunderstood, of course, that this disclosure is not limited to theparticular embodiments illustrated herein.

DETAILED DESCRIPTION OF INVENTION

As discussed, above, Rapid Manufacturing Techniques (RMT) such as DirectMetal Fabrication (DMF) can be used to produce porous structures formedical implants. However, using DMF or other RMT to fabricate porousstructures can create weak areas between fenestrations of thethree-dimensional porous structure. This is mostly due to the shapes andconfigurations of the cells that have been used in the prior art to formthese porous structures. In particular, fractures typically occur atareas where struts are connected together at a node. The fractures occurin porous structures of the prior art because the cross-sectional areaof a strut where it connects to the node is typically less than thecross-sectional area of the resulting node. The areas where the strutsconnect to their node, typically referred to as stress risers, arecommon points of structural failure. The pattern of failure at thestress risers can also occur when the molten phase of particles does notcompletely melt and fuse together or when the surrounding substratesurfaces is too cold, which causes the hot powdered material to bead upduring the DMF process. Regardless of the exact causes of strutfractures and the resulting poor performance of porous structures of theprior art, improved porous structures that can be fabricated using RMT,including DMF, and other free-form fabrication and near net-shapeprocesses (e.g., selective laser sintering, electron beam melting, andstereo-lithography) are desired.

FIGS. 1A and 1B provide an illustration of where fractures may occur.FIGS. 1A-1B illustrate an example of a porous structure with three orfour struts, respectively, connected at a single node, where the strutsof FIG. 1A have the same diameters and the struts of FIG. 1B havedifferent diameters. Specifically, in FIG. 1A, three struts 102 ofgenerally equal diameters are connected together at node 104. Threestress risers 106 are created at the connections between the threestruts 102. Because the cross-sectional diameters of struts 102 at thestress risers 106 are less than the cross-sectional diameter of the node104, the stress risers 106 are locations for a typical strut failure. InFIG. 1B, three smaller struts 108 are connected to a larger strut 110 ata node 112. Three of the four resulting stress risers are shown at 114,which have substantially smaller cross-sectional diameters than the node112. FIG. 2 is a SEM (Scanning Electron Microscope) microphotograph of astructure 200 fabricated using RMT, and it shows an example of strutfracture surfaces 202. In FIG. 2 , the sample shown is occluded withbuild powder 204 in the areas around the strut fracture surfaces 202.

Referring to FIGS. 3-5 , various embodiments of the present inventionare shown. In FIGS. 3-5 , struts 302, 402, and 502 are connectedtogether at their respective nodes 304, 404, and 504 in variouscombinations. Each of nodes 304, 404, and 504 is a connection betweenonly two struts. For example, in FIG. 5 , node 504 a comprises aconnection between struts 502 a and 502 b; node 504 b comprises aconnection between struts 502 b and 502 c; and node 504 c comprises aconnection between struts 502 b and 502 d. By reducing the number ofstruts 302, 402, and 502 that meet or are connected at their respectivenodes 304, 404, and 504, the diameter or cross-sectional area where thestruts 302, 402, and 502 are connected is substantially equal to thecross-sectional area at the respective nodes 304, 404, and 504.Therefore, the effect of the stress risers (not shown) on the strengthof the structure is lessened in the structures illustrated in FIGS. 3-5. Consequently, the resulting structures are substantially stronger thanthe structures of the prior art illustrated in FIGS. 1A-1B.

FIGS. 6-8 illustrate alternative embodiments of the porous structures ofthe present invention comprising strut and node combinations where atleast some of the struts are characterized by a smaller cross-sectionaldiameter at the body of the strut than at the stress riser. The struts602, 702, and 802 are characterized by a fluted or conical shape whereeach of struts 602, 702, and 802 flares to a wider cross-sectionaldiameter as the strut approaches and connects at the respective nodes604, 704, and 804. The designs of FIGS. 6-8 illustrate incorporatefluted struts 602, 702, and 802 and non-fluted struts 606, 706, and 806,where both types of struts are connected at the respective nodes 604,704, and 804.

Thus, each of the connections between the fluted struts 602, 702, and802 and the non-fluted struts 606, 706, and 806 has a cross-sectionaldiameter that is essentially equivalent to the maximum cross-sectionaldiameter of fluted struts 602, 702, and 802. Accordingly, the effect ofthe stress risers (not shown) of the structures are thereby reduced.Referring to FIG. 9A, it is a plan view of the struts 802 and nodes 804in FIG. 8 . FIG. 9B is a plan view of an individual node in FIGS. 6-8 ,which is labeled as struts 602 and node 604 for demonstrative purposes.Referring to FIGS. 9A-9B, the fluted struts 602, 802 have a larger ormaximum cross-sectional diameter at the ends 606, 806 that meet at thenodes 804, 604, and a smaller or minimum cross-sectional diameter at themiddle portions. Thus, the effect of stress risers (not shown) at thejunctions between the struts fluted struts 602, 702, and 802 and thenon-fluted struts 606, 706, and 806 are reduced. Preferably, only twostruts, e.g., 602 and 606, meet any given node, e.g. 604, for addedstrength.

FIGS. 10A-10F illustrate 2-D representations of various configurationsof the frame of the struts and nodes in a porous structure of the priorart. For simplification purposes, the struts are not represented in 3-Dbut rather each strut is represented by a different line, e.g., itsframe, that is either solid, bolded solid, or dashed lines. Thisrepresentation is simply exemplary and not meant to be limiting. In theprior art, it is typical for a porous structure to have more than twostruts meeting at a node 1002, regardless whether the strut may bestraight, curved, or irregular. While FIG. 10A may show two strutsmeeting at a node, the stress risers of this configuration has theeffect of the stress risers at a node with four struts connecting orintersecting one another. For example, U.S. Publication Nos.2006/0147332 and 2010/0010638 show examples of these prior artconfigurations employed to form porous structures.

In contrast, to the prior art configurations of FIGS. 10A-10F, thepresent invention reduces the effect of the stress risers at the nodesby ensuring that no more than two struts intersect at a node.Consequently, some embodiments result in the diameter or cross-sectionalarea where the struts intersect being substantially equal to thecross-sectional area at each node, thereby reducing the effect of thestress risers on the strength of the structure. FIGS. 11A-11F illustrateexemplary embodiments of the present invention for modifying thecorresponding configuration of the prior art to ensure that no more thantwo struts intersect at a node. As seen in FIGS. 11A-11F, each of thenodes 1102 has only two struts intersecting. For simplificationpurposes, only one of the numerous nodes in 11A-11F is labeled with thenumber 1102. In particular, the FIGS. 11A-11F show at nodes 1102, theend of one strut intersect the body of another strut. Further, themodification of the prior art configurations according to one embodimentof the present invention forms a modified pore 1104 that is open in eachconfiguration that provides additional porosity with added strength,which is a great improvement over the prior art. FIGS. 12A-12Dillustrate 3-D representations of exemplary embodiments of the porousstructure of the present invention formed with one or moreconfigurations in FIGS. 11A-11F, where the frames, e.g., lines, havebeen given a thickness to form struts. In FIGS. 12A-12D, the porousstructures have struts 1202 that intersect one another at nodes 1204where no more than two nodes intersect at a node.

As demonstrated by FIGS. 11A-11F, the conventional nodes 1002 of FIGS.10A-10F are effectively being “opened” up to ensure that no more thantwo struts meet at a node. In addition to reducing the effect of stressrisers at the node, this “opening” up of the conventional nodes 1002 ofFIGS. 10A-10F into nodes 1102 of FIGS. 11A-11F has the added benefit ofreducing heat variations during the fabrication process. As with anyother thermal processes, being able to control the heat variations,e.g., cooling, of the material is important to obtain the desiredmaterial properties.

Referring to FIGS. 13A-13M, the present invention also provides forembodiments that reduce the effect of stress risers by incorporatingcurved struts into the porous structures. FIGS. 13A-13M illustrate 2-Drepresentations of these various exemplary configurations of the frameof the two struts of the present invention forming a node, includingframes for struts that are straight, curved, or a combination of both.As shown, only two struts intersect each other at the node 1302. Atleast in FIGS. 13A-13C, the struts intersect one another tangentially atthe node 1302, providing increased mechanical strength and bonding. FIG.14 illustrates 2-D representation of an exemplary embodiment of theporous structure of the present invention comprising one or more frameconfigurations in FIGS. 13A-13M, including frames for struts that arestraight, curved, or a combination of both. As shown by FIG. 14 , nomore than two struts, whether curved or straight, meet at each node.FIGS. 15A-15C illustrate 2-D representations of exemplary configurationsof the present invention of various curved frames and correspondingstruts intersecting to form a node 1502. In FIGS. 15A-15C, the dashedlines represent the frames 1504 and the solid lines represent thecorresponding struts 1506. As shown, node 1502 a is formed where thecircular strut with its center at 1508 tangentially intersect or meetthe circular strut with its center at 1510. The node 1502 b is formedwhere the circular strut with its center at 1508 tangentially intersector meet the circular strut with its center at 1512. Similarly, FIG. 15Bshows the circular strut with its center at 1514 tangentiallyintersecting the circular strut with its center at 1516 to form node1502 c. Likewise, FIG. 15C shows the circular strut with its center at1518 tangentially intersecting the circular strut with its center at1520 to form node 1502 d. FIG. 16 illustrates a 3-D representation of anexemplary embodiment of the porous structure of the present inventioncomprising one or more frame configurations in FIGS. 13A-13M, includingframes for struts that are straight, curved, or a combination of both.

FIG. 17 illustrates a 3-D representation of an exemplary frame for agenerally cubical cell 1700 formed by twelve struts 1702 and sixteennodes 1704. Again, for simplification purposes, only some of the strutsand nodes are labeled. By using sixteen nodes 1704 that form connectionsbetween only two struts 1702 as opposed to eight nodes that formconnections between three struts as in a conventional cube design (notshown), the cell 1700 provides stronger nodes 1704, and strongerconnections between the struts 1702 and nodes 1704. As a result, thisnovel configuration of one embodiment of the present invention avoidsvariations in cross-sectional diameters between struts 1702 and nodes1704. As a result, the negative effects of stress risers like thoseshown at stress risers 106 and 114 in FIGS. 1A-1B on the strength of thestructure are lessened. FIG. 18 illustrates a porous structure 1800formed from a plurality of connected cells 1802, which are similar tothose shown in FIG. 17 . Similarly, FIGS. 19-20 show another comparisonbetween the arrangement of cells of the prior art in FIG. 19 and oneembodiment the arrangement of cells of the present invention in FIG. 20. As previously discussed, by having more than two struts intersect at anode, the porous structure of the prior art is weak due to the increasedeffect of the stress risers. On the other hand, the arrangement in FIG.20 of the present invention provides the requisite porosity with animproved strength because no more than two struts intersect at a node.In addition, the arrangement of FIG. 20 has the added benefit of havingmore trabecular features, resembling the characteristics of cancellousbone, unlike the regular prior art configuration. Moreover, theadvantage of looking trabecular while being formed in a calculatedmanner provides another benefit to the porous structures formed inaccordance with the invention a decreased need for expansiverandomization of the porous structure. Consequently, the arrangement ofFIG. 20 resembles the characteristics of bones more so than the priorart configuration of FIG. 19 . FIG. 21 is a blown up view of thearrangement in FIG. 20 where the dashed lines 3102 represent the framesof the struts to better show where the struts meet to form a node.

Similarly, FIG. 22 illustrates another embodiment of a cell of thepresent invention. Cell 2200 is based on a tetrahedron-shaped cell, or atriangular pyramid, where it is formed using only six struts 2202 andeight nodes 2204. Each node 2204 connects only two struts 2202 together.FIG. 23 illustrates a similar cell 2300, which is a square-basedpyramid. Referring to FIG. 23 , eight struts 2302 and eleven nodes 2304are used to form the cell 2300. Other geometrical shapes for cells, suchas dodecahedrons, icosahedrons, octagonal prisms, pentagonal prisms,cuboids, and various random patterns are discussed below. In addition,FIGS. 17, 18, 22 and 23 illustrate frames of struts that can be builtfrom these frames where the thickness of each strut can be selected. Assuch, the thickness for each strut can be uniform or vary from one strutto another strut. Further, the struts can incorporate the fluted startsof FIGS. 6-8 . In addition, the struts do not have to be cylindrical inshape. As further discussed below, the cross-section of the struts canbe rectangular or square or any other shape, e.g., geometric shape orirregular shapes, that would be suitable for the application.

As discussed above with respect to FIGS. 17, 18, 22, and 23 , variouscell designs of various shapes can be created using various techniquesdiscussed above, e.g., DMF. Generally speaking, almost anythree-dimensional multiple-sided design may be employed. For example,cells with an overall geometric shape such as Archimedean shapes,Platonic shapes, strictly convex polyhedrons, prisms, anti-prisms, andvarious combinations thereof are within the contemplation of the presentinvention. In other embodiments, the number of sides of each cell mayrange from about 4 to about 24. More preferably, the number of sides-ofeach cell may range from about 4 to about 16. One geometry that has beenfound to be particularly effective is a dodecahedron or 12 sided cell.However, as explained and illustrated below, the geometries of theindividual cells or the cells of the porous structure may vary widelyand, in the geometries, may vary randomly from cell to cell of a porousstructure.

For example, FIGS. 24A and 24B illustrate a conventionally designeddodecahedral cell 2400 from a prior art porous structure with each node2404 being a connection between, three struts 2402. Again, U.S.Publication. Nos. 2006/0147332 and 2010/0010638 disclose examples ofporous structures formed from these conventional cells. A porousstructure with a given porosity and having a desired volume can beformed using a plurality of cells 2400 by attaching one cell 2400 toanother cell 2400 until the desired volume is achieved. Further, thestructures using the prior art cell configuration, may bedisadvantageous because they do not resemble the randomness of nativecancellous structures. That is, they do not adequately resemble thefeatures of trabecular bone. More importantly, referring to FIGS. 24Aand 24B, higher stresses are placed at each node 2404 because the struts2402 intersect one another at 120.degree. angles, thereby increasingstress concentration factors due to the formation of notches or grooveson the face of the nodes 2404 and the connection between more than twostruts 2402 at each node 2404.

FIGS. 25A and 25B illustrate one embodiment of the present inventionthat provides a solution to these problems of the prior art. As shown byFIGS. 25A and 25B, cell 2500 eliminated the conventional nodes 2404 inFIGS. 24A and 24B by using curved struts 2502 that form a ring or hoop,thereby eliminating the stress concentration factors caused by thesenodes. In addition, cells 2500 replace conventional nodes 2404 in FIGS.24A and 24B with modified nodes 2504 that can be open or porous toprovide additional porosity, which is an added benefit for manyapplications, such as enhancing tissue/bone ingrowth for orthopedicimplants. Accordingly, cell 2500 provides additional strength withincreased porosity while the conventional cell 2400 is weaker and lessporous.

FIGS. 26-28 illustrate one embodiment to forming the cell in FIGS. 25Aand 25B. FIG. 26 illustrates a dodecahedral frame 2600 for prior artcells as discussed with respect to FIGS. 24A and 248 . FIG. 27illustrates frame 2700 which comprises frame 2800 of FIG. 28superimposed over the dodecahedral frame 2600 of FIG. 26 . FIG. 29Aillustrates a cell similar to that of FIGS. 25A and 25B formed byselecting a thickness for frame 2800. In FIG. 29A, the cell 2900 isconstructed from twelve curved struts 2902 that, in this embodiment, mayform a ring, a loop, an annulus, or a hoop. The curved struts 2902 arejoined together at triangular modified nodes 2904 that are more easilyseen in FIG. 29B. Referring to FIG. 29B, the thicker circles representfour of the curved struts 2902 of the cell 2900 while the thinnercircles highlight the modified nodes 2904 formed by struts 2902. Eachmodified node 2904 includes three fused connections or sinteringjunctions 2906 between two different curved struts 2902. That is, curvedstruts 2902 tangentially intersect one another at the respectivejunction 2906. Depending on the thickness of each strut 2902, modifiednode 2904 may also be porous with openings 2908 disposed between thethree junctions 2906 or occluded with no openings disposed between thethree junctions 2906. Preferably, modified node 2904 has openings 2908disposed between the three junctions 2906 to provide additional porosityin conjunction with the porosity provided by the fenestrations 2910 ofthe curved struts 2902. Referring to FIG. 29B, while the struts 2906tangentially intersect one another, e.g., their frame tangentially meet,the struts' thickness may render the individual junctions 2906relatively long as indicated by the distance 2912. These long, generallytangential sintering junctions 2906 provide increased mechanicalstrength and bonding.

Referring to FIG. 30 . it depicts an unfolded or flattenedtwo-dimensional representation of FIG. 27 , with conventional frame 3008and the frame 3010 of cell 2900. As shown by FIG. 30 , the location andnumber of individual junctions 3006, as compared to conventional nodes3004 of the conventional configuration 3008, is different when usingcurved struts 3002 provided by the invention. For example, junctions3006 are generally located around the center of the body of curvedstruts 3002, while conventional nodes 3002 is located at the end of theconventional struts. In addition, in this particular embodiment, thenumber of junctions 3006 where the curved struts 3002 meet is threetimes the number of conventional nodes 3004 where straight struts meetfor frame 3008. Accordingly, the increased number of junctions provideincreased mechanical strength.

FIGS. 31-34 illustrate how frames for cells based on a typicalpolyhedron can be modified with curved struts to form a cell similar tocell 2900 of FIG. 29 . Specifically, FIG. 31 illustrates a frame 3100 ofa truncated tetrahedral cell unfolded into a 2-D representation. In FIG.32 , frame 3202 represents frame 3100 of FIG. 31 as modified by oneembodiment the present invention to be formed with curved struts 3202.Similarly, FIG. 33 Illustrates the frame 3300 of a truncated octahedralcell unfolded into a 2-D representation, and frame 3402 of FIG. 34represents frame 3300 of FIG. 31 as modified by one embodiment thepresent invention to be formed with curved struts 3402. As discussedabove, e.g., with respect to FIG. 30 , the cells formed with frames 3200and 3400 have increased mechanical strength and porosity over frames3100 and 3300, respectively.

FIGS. 35A-35B illustrate one way of modifying a typical polyhedron framewith curved struts. According to one embodiment of the invention, thepolyhedron can be modified by inscribing, within the polyhedron, acircle or other shapes that contain curved features, such as an ellipseor oblong. Specifically, FIG. 35A is a circle inscribed within a square,FIG. 35B is a circle inscribed within a hexagon, FIG. 35C is a circleinscribed within a triangle, FIG. 35D is a circle inscribed within anoctagon, and FIG. 35E is an oval inscribed within a parallelogram. FIGS.35A-35B are merely demonstrative of the different configurationsavailable and are not intended to limit the scope of the invention.

FIG. 36 illustrates another way of modifying a typical polyhedron framewith curved struts. According to another embodiment of the invention,the polyhedron can be modified by circumscribing the polyhedron with acircle or other shape that contain curved features, such as an ellipseor oblong. FIG. 36 illustrates a frame 3600 of a truncated tetrahedralcell with circles 3602 circumscribed around each face of the cell. Someor all portions of frame 3600 may be removed to form a new cell framethat can be used to fabricate a porous structure according to thepresent invention.

FIGS. 37-39 illustrate embodiments of the present invention thatincorporate both straight and curved struts. Specifically, FIGS. 37A and37B illustrate cell 3700 formed from frame 2700 of FIG. 27 , which is acombination of the dodecahedral frame 2600 of FIG. 26 with frame 2800 ofFIG. 28 . Cell 3700 has increased strength due to the addition of thecurved struts, which result in a blending of the stress risers. Asshown, cell 3700 has modified node 3704 comprising a conventional nodeformed with straight struts 3702 b and a node formed by three junctionsof the curved struts 3702 a. FIG. 38 illustrates cell 3800 formed bykeeping one or more conventional nodes 3804 formed by straight struts3802 while modifying the other struts of the cells with curved struts3806 to form junctions 3808 and modified nodes 3810. In FIG. 38 somestruts are selectively thicker than other struts, depending onapplications.

Referring to FIG. 38 , the cell 3800 has at least one curved strut 3802,and preferably a plurality of curved struts 3802 that form modified node3804 a when joined with two other curved struts 3802. In otherembodiments, the modified nodes can be formed by joining together curvedstruts, curbed strut sections, straight struts, or straight sections, orcombinations thereof. An example of a node formed by joining togetherstraight and curved struts is shown in FIGS. 39A-39C as modified node3904 b. Modified nodes 3804 a are preferably triangular formed by threejunctions 3806. Cell 3800 may contain some convention nodes 3808 thatjoin straight struts 3810 or straight strut sections that may comprisenotches formed by intersecting angles practiced in the prior art. Themodified node 3804 a may be porous as discussed previously and indicatedby 3804 a or occluded as indicated at 3804 b. The occluded modifiednodes 3804 b and the porous modified nodes 3804 a may be formed bytangent sintering three or more junctions 3806 between curved or“ring-like”0 struts together. Any combination of occluded nodes 3804 b,porous modified nodes 3804 a, conventional nodes 3808, straight struts3810, curved struts 3802, and portions or segments thereof may be usedin different predetermined or random ways in order to create stronger,more cancellous-appearing cell structure. Referring to FIGS. 39A-39C,cell. 3900 is an example of such combination. Cell 3900 has curvedstruts 3902 a that are “ring-like” and struts 3902 b. It also hasstraight struts 3906 and conventional nodes 3908. The combination ofstruts forms porous modified nodes 3904 a and occluded modified nodes3964 b.

Thus, while the cells 3800 within a porous structure may be homogeneous,they may be arranged in a random and/or predetermined fashion withrespect to each other to more closely resemble the appearance ofcancellous bone. In some instances, it may be desirable to utilize oneor more heterogeneous cell configurations which may be arrangedsystematically in predetermined patterns and/or arranged in randomfashion to create a porous structure. Various arrangements can bedesigned using computer aided design (CAD) software or other equivalentsoftware as will be apparent to those skilled in the art.

FIGS. 40 and 41 show exemplary configurations of how the cells 2400,2900, and 3700 from FIGS. 24, 29, and 37 , respectively, can becombined, e.g., attached, joined, tiled, stacked, or repeated.Specifically, FIG. 40 illustrates arrangement 4000 comprising cell 2400and cell 2900 from FIGS. 24 and 29 , respectively. In arrangement 4000,at the face where cell 2400 attaches to cell 2900, conventional nodes2404 is placed partially within modified nodes 2904. Accordingly, byusing various combinations of cells 2400 and cells 2900, or other cellsformed according to the present invention, a number of modified nodes2504 can be selectively occluded completely or partially by matchingconventional nodes with modified nodes. FIGS. 41A and 41B illustratearrangement 4100 comprising cells 2400, 2900, and 3700. Again, FIGS. 40and 41 are illustrative and do not limit the combination that can bemade with these cells or other cells formed according to the embodimentsof the present invention.

FIG. 42 illustrates a porous structure 5300 formed by joining aplurality of cells 4202 together, where the shape of cells 4202 is basedon a truncated tetrahedron. One or more curved struts 4204 which may ormay not form complete rings are inscribed within, or circumscribedaround, each face of the selected polyhedral shape, which is a truncatedtetrahedron in FIG. 42 . Alternatively, the truncated tetrahedron shapeor other selected polyhedral shape may be formed using a large number ofshort straight struts to closely approximate truly curved ring struts,such as the ring struts of cell 2900 in FIG. 29 .

FIGS. 43-45 illustrate 3-D representations of exemplary arrangementscells formed in accordance with the embodiments of the presentinvention. Specifically, FIG. 43 illustrates one way cells based ontruncated octahedra can be stacked to form bitruncated cubic honeycombstructure 4300, which is by space-filling tessellation. The cells ofstructure 4300 in both shades of gray are truncated octahedra. Forsimplification purposes, each cell is not modified with a curved strutbut rather the dashed circle serves to illustrate that one or more facesor one or more truncated octahedra can be modified according to theembodiments of the present invention, e.g., curved struts to form porousstructures with increased strength and porosity. Similarly, FIG. 44illustrates one way, e.g., space-filling tessellation, cells based on acombination of cubes (light grey), truncated cuboctahedra (black), andtruncated octahedra (dark grey) can be stacked to form cantitruncatedcubic honeycomb structure 4400. Again, it is understood that the dashedcircles represent how one or more polyhedron of porous structure 4400can be modified according to the embodiments of the present invention,e.g., curved struts to form porous structures with increased strengthand porosity. Likewise, FIG. 45 illustrates one way, e.g., space-fillingtessellation, cells based on a combination of cuboctahedra (black),truncated octahedra (dark grey) and truncated tetrahedra (light grey)can be stacked to form truncated alternated cubic honeycomb structure4500. Again, it is understood that the dashed circles represent how oneor more polyhedron of structure 4500 can be modified according to theembodiments of the present invention, e.g., curved struts to form porousstructures with increased strength and porosity.

FIG. 46 illustrates a frame view of the bitruncated cubic honeycombstructure 4300 of FIG. 43 . FIG. 47 illustrates a frame viewcantitruncated cubic honeycomb structure 4500 of FIG. 45 . As shown byFIGS. 46 and 47 , porous structures formed with polyhedral are notrandom, and thus, are not as suitable for implantation purposes,particularly for bones, because they do not adequately resemble thefeatures of trabecular bone. On the other hand, as it can be envisionedthat modifying certain or all cells of the frames in FIGS. 46 and 47would result in porous structures resembling trabecular bone.

When curved struts are employed, at least one curved strut portion maygenerally form a portion of a ring which at least partially inscribes orcircumscribes a side of a polyhedron. Such a polyhedral shape may be anyone of isogonal or vertex-transitive, isotoxal or edge-transitive,isohedral or face-transitive, regular, quasi-regular, semi-regular,uniform, or noble. Disclosed curved strut portions may also be at leastpartially inscribed within or circumscribed around one or more sides ofone or more of the following Archimedean shapes; truncated tetrahedrons,cuboctahedrons, truncated cubes (i.e., truncated hexahedrons), truncatedoctahedrons, rhombicuboctahedrons (i.e., small rhombicuboctahedrons),truncated cuboctahedrons (i.e., great rhombicuboctahedrons), snub cubes(i.e., snub hexahedrons, snub cuboctahedrons—either or both chiralforms), icosidodecahedrons, truncated dodecahedrons, truncatedisosahedrons (i.e., buckyball or soccer ball-shaped),rhombicosidodecahedrons (i.e., small rhombicosidodecahedrons), truncatedicosidodecahedrons (i.e., great rhombicosidodecahedrons), snubdodecahedron or snub icosidodecahedrons (either or both chiral forms).Since Archimedean shapes are highly symmetric, semi-regular convexpolyhedrons composed of two or more types of regular polygons meeting inidentical vertices, they may generally be categorized as being easilystackable and arrangeable for use in repeating patterns to fill up avolumetric space.

In some embodiments, curved strut portions according to the inventionare provided to form a porous structure, the curved strut portionsgenerally forming a ring strut portion at least partially inscribingwithin or circumscribing around one or more polygonal sides of one ormore Platonic shapes (e.g., tetrahedrons, cubes, octahedrons,dodecahedrons, and icosahedrons), uniform polyhedrons (e.g., prisms,prismatoids such as antiprisms, uniform prisms, right prisms,parallelepipeds, and cuboids), polytopes, polygons, polyhedrons,polyforms, and/or honeycombs. Examples of antiprisms include, but arenot limited to square antiprisms, octagonal antiprisms, pentagonalantiprisms, decagonal antiprisms, hexagonal antiprisms, and dodecagonalantiprisms.

In yet other embodiments, a porous structure may be formed from cellscomprising the shape of a strictly convex polyhedron, (e.g., a Johnsonshape), wherein curved strut portions generally form a ring strutportion at least partially inscribed within or circumscribed around oneor more face of the strictly convex polyhedron, wherein each face of thestrictly convex polyhedron is a regular polygon, and wherein thestrictly convex polyhedron is not uniform (i.e., it is not a Platonicshape, Archimedean, shape, prism, or antiprism). In such embodiments,there is no requirement that each face of the strictly convex polyhedronmust be the same polygon, or that the same polygons join around eachvertex. In some examples, pyramids, cupolas, and rotunda such as squarepyramids, pentagonal pyramids, triangular cupolas, square cupolas,pentagonal cupolas, and pentagonal rotunda, are contemplated. Moreover,modified pyramids and dipyramids such as elongated triangular pyramids(or elongated tetrahedrons), elongated square, pyramids (or augmentedcubes), elongated pentagonal pyramids, gyroelongated square pyramids,gyroelongated pentagonal pyramids (or diminished icosahedrons),triangular dipyramids, pentagonal dipyramids, elongated triangulardipyramids, elongated square dipyramids (or biaugmented cubes),elongated pentagonal dipyramids, gyroelongated square dipyramids may beemployed. Modified cupolas and rotunda shapes such as elongatedtriangular cupolas, elongated square cupolas (diminishedrhombicuboctahedrons), elongated pentagonal cupolas, elongatedpentagonal rotunda, gyroelongated triangular cupolas, gyroelongatedsquare cupolas, gyroelongated pentagonal cupolas, gyroelongatedpentagonal rotunda, gyrobifastigium, triangular orthobicupolas (gyratecuboctahedrons), square orthobicupolas, square gyrobicupolas, pentagonalorthobicupolas, pentagonal gyrobicupolas, pentagonal orthocupolarotunda,pentagonal gyrocupolarotunda, pentagonal orthobirotunda (gyrateicosidodecahedron), elongated triangular orthobicupolas, elongatedtriangular gyrobicupolas, elongated square gyrobicupolas (gyraterhombicuboctahedrons), elongated pentagonal orthobicupolas, elongatedpentagonal gyrobicupolas, elongated pentagonal orthocupolarotunda,elongated pentagonal gyrocupolarotunda, elongated pentagonalorthobirotunda, elongated pentagonal gyrobirotunda, gyroelongatedtriangular bicupolas (either or both chiral forms), gyroelongated squarebicupolas (either or both chiral forms), gyroelongated pentagonalbicupolas (either or both chiral forms), gyroelongated pentagonalcupolarotunda (either or both chiral forms), and gyroelongatedpentagonal birotunda (either or both chiral forms) may be utilized.Augmented prisms such as augmented triangular prisms, biaugmentedtriangular prisms, triaugmented triangular prisms, augmented pentagonalprisms, biaugmented pentagonal prisms, augmented hexagonal prisms,parabiaugmented hexagonal prisms, metabiaugmented hexagonal prisms, andtriaugmented hexagonal prisms may also be practiced with the invention.Modified Platonic shapes such as augmented dodecahedrons,parabiaugmented dodecahedrons, metabiaugmented dodecahedrons,triaugmented dodecahedrons, metabidiminished icosahedrons, tridiminishedicosahedrons, and augmented, tridiminished icosahedrons may be employed.Moreover, modified Archimedean shapes such as augmented truncatedtetrahedrons, augmented truncated cubes, biaugmented truncated cubes,augmented truncated dodecahedrons, parabiaugmented truncateddodecahedrons, metabiaugmented truncated dodecahedrons, triaugmentedtruncated dodecahedrons, gyrate rhombicosidodecahedrons, parabigyraterhombicosidodecahedrons, metabigyrate rhombicosidodecahedrons, trigyraterhombicosidodecahedrons, diminished rhombicosidodecahedrons, paragyratediminished rhombicosidodecahedrons, metagyrate diminishedrhombicosidodecahedrons, bigyrate diminished rhombicosidodecahedrons,parabidiminished rhombicosidodecahedrons, metabidiminishedrhombicosidodecahedrons, gyrate bidiminished rhombicosidodecahedrons,and tridiminished rhombicosidodecahedrons are envisaged. Snubdisphenoids (Siamese dodecahedrons), snub square antiprisms,sphenocorona, augmented sphenocorona, sphenomegacorona,hebesphenomegacorona, disphenocingulum, bilunabirotunda, and triangularhebesphenorotunda and other miscellaneous non-uniform convex polyhedronshapes are contemplated.

In some embodiments, the average cross section of the cell fenestrationsof the present invention is in the range of 0.01 to 2000 microns. Morepreferably, the average cross section of the cell fenestrations is inthe range of 50 to 1000 microns. Most preferably, the average crosssection of the cell fenestrations is in the range of 100 to 500 microns.Cell fenestrations can include, but are not limited to, (1) any openingscreated by the struts such as the open modified pores, e.g., 3804 a ofFIG. 38 or 1104 of FIGS. 11A-11F, created by the junctions, e.g., 3806of FIG. 38 or nodes 1102 of FIGS. 11A-11F, or (2) any openings inscribedby the struts themselves, e.g., 2910 of FIG. 29B. For example, inembodiments where the cell fenestrations are generally circular, theaverage cross section of a fenestration may be the average diameter ofthat particular fenestration, and in embodiment where the cellfenestrations are generally rectangular or square, the average crosssection of a fenestration may be the average distance going from oneside to the opposite side.

Applying the above principles to other embodiments. FIGS. 51A and 51Billustrate a cell 5100 formed from an octahedron frame shown in FIG. 48modified according to one embodiment of the present invention, shown inFIGS. 49-50 . In FIG. 49 , frame 4900 is formed by inscribing circleswithin the faces of frame 4800 in FIG. 48 . In FIG. 50 , frame 5000 isformed by removing frame 4800 from frame 4900 of FIG. 49 . As shown inFIG. 49 , the frame 5000 generally fits within the octahedron frame4800. FIGS. 51A and 51B illustrate the completed cell 5100, which isformed by selecting a shape and thickness for frame 5000 in FIG. 50 .Referring to FIGS. 51A and 51B, cell 5100 generally comprises eightcurved struts 5102 that may be provided in the form of rings. The eightcurved struts 5102 are connected to one another at twelve differentjunctions 5106. Six porous modified nodes 5104, each modified nodehaving a generally rectangular shape are formed by the four differentjunctions 5106 and the corresponding struts 5102. As shown by FIGS. 51Aand 51B, unlike the curved struts of cell 2500 of FIGS. 25A and 25B,curved struts 5102 have a rectangular or square cross-section ratherthan a circular cross-section of cells similar to cells 2500 in FIGS.25A and 25B. Cells with a rectangular or square cross-section providethe porous structure with a roughness different than that of the cellswith a circular cross-section. It is envisioned that struts of otherembodiments can have different shapes for a cross-section. Accordingly,the struts of a cell can have the same cross-section, the shape of thecross-section of the struts can be randomly chosen, or the cross-sectionshape can be selectively picked to achieve the strength, porosity,and/or roughness desired.

As another alternative, FIGS. 53A-53D illustrate yet another cell 5300based on a truncated tetrahedron frame shown in FIG. 52 as modified byone embodiment of the present invention. Referring to FIGS. 53A-53D, thecell 5300 is formed in a similar manner to cell 5100 of FIGS. 51A and51B. That is, frame 5200 is inscribed with circles to form a secondframe comprising circular struts, and frame 5200 is removed leavingbehind the circular frame. Cell 5300 is completed by selecting athickness and shape of the cross-sectional area for the frame 5300. Asdiscussed above, the thickness and shape of the cross-section of thestruts can be uniform or it can vary randomly or in a predeterminedmanner, including struts with a uniform cross-section or struts that arefluted. Cell 5300 includes four larger curved struts 5302 a thatcorrespond with the four large hexagonal sides of the truncatedtetrahedral frame 5200 and four smaller curved struts 5202 b thatcorrespond with the four smaller triangular sides of the truncatedtetrahedral frame 5200. Alternative, a cell can be formed bycircumscribing a circle about the large sides 5202 and small sides 5204of the truncated tetrahedral frame 5200. A 2-D representation of thisalternative embodiment is shown in FIG. 36 . While not expressly shownin the drawings, it is also contemplated that in some embodiments,combinations of inscribed and circumscribed curved struts may beemployed. As illustrated in FIGS. 53A-53D, porous triangular modifiednodes 5304 are formed between three junctions 5306 that connect thestruts 5202 a and 5202 b together, but those skilled in the art willrecognize that occluded modified nodes 3804 b as shown in FIG. 38 mayalso be employed. Also, as shown in FIGS. 53A-53D, larger curved struts5302 a have a circular cross-section while smaller curved struts 5302 bhave a rectangular cross-section. FIGS. 54A-54E illustrate variousangles of a porous structure formed by stacking cells 5300 of FIG. 53 inone exemplary manner. It is envisioned that that in some embodiments,cells 5300 of FIG. 53 can be stacked in different manners as known be aperson skilled in the art.

FIGS. 55A-55E illustrate yet another embodiment where a cell 5500 isbased on a hexagonal prism (Prismatic) frame with upper and lowerhexagons and that includes six vertical sides. The six smaller curvedstruts 5502 a are used for the six sides and larger upper and lowercurved struts 5502 b are used for the top and bottom. In the cell 5500illustrated in FIGS. 55A-55E, the eight curved struts 5302 a, 5302 b areconnected by occluded modified nodes 5504 but, it will be apparent tothose skilled in the art that porous modified nodes such as those shownin FIG. 25 may also be employed. In the particular embodiment shown inFIGS. 55A-55E, the six smaller curved struts 5502 a used for the sixsides have a slightly smaller cross-sectional area than the two largerupper and lower curved struts 5302 b. However, it would be apparent tothose skilled in the art that the struts with uniform or substantiallyuniform cross-sectional areas can also be employed without departingfrom the scope of this disclosure. FIGS. 56A-56B illustrate variousangles of a porous structure formed by stacking cells 5500 of FIGS.55A-55E in one exemplary manner. In FIGS. 56A and 56B, cells 5500 areplaced adjacent to one another to form a layer 5602 and the layers areplaced on top of one another either in a predetermined or random manner.FIGS. 57A and 57B similarly show a greater number of cells 5500 stackedin the same manner as shown in FIGS. 56A and 56B. As seen, cells 5500are stacked by layers 5702. It is envisioned that in some embodiment,cells 5500 of FIG. 55 can be stacked in different manners as known to aperson skilled in the art.

FIGS. 58-61 illustrate dodecahedral frames 5800, 5900, 6000, and 6100modified according to another embodiment of the invention. Instead ofusing curved struts or struts with curved portions to eliminate orreduce conventional nodes 5802, 5902, 6002, and 6102, the particularembodiments of FIGS. 58-61 adjust the conventional nodes by ensuring atleast one of the conventional nodes have no more than two nodeintersecting at a node as shown by at least FIGS. 11A-11F. As shown byFIGS. 58-61 , frames 5800, 5900, 6000, and 6100 have at least onemodified node 5804, 5904, 6004, and 6104.

In some embodiment, the configurations of the cells, struts, nodesand/or junctions may vary randomly throughout the porous structure tomore closely simulate natural bone tissue. Particularly, the cellsformed according to the present invention, such as the cells illustratedin FIG. 25A-25B, 29A, 37A-37B, 38, 39A-39C, 42, 51A-51B, 53A-53D, or35A-55B, can be stacked or repeated according to the methods outlined inU.S. Application No. 61/260,811, the disclosure of which am incorporatedby reference herein in its entirety. In addition, the methods of U.S.Application No. 61/260,811 can also be employed to modify conventionalnodes such that no more than two struts intersect at a node. In yetanother embodiment, the porous structure formed according to theinvention can be used in medical implants, such as an orthopedicimplant, dental implant, or vascular implant.

As further discussed in the following paragraphs, the present disclosurealso provides for a method to fabricate the porous structures describedabove. Preferably, the improved porous structures of the presentinvention is formed by using a free-form fabrication method, includingrapid manufacturing techniques (RMT) such as direct metal fabrication(DMF). Generally, in free-form fabrication techniques, the desiredstructures can be formed directly from computer controlled databases,which greatly reduces the time and expense required to fabricate variousarticles and structures. Typically in RMT or free-form fabricationemploys a computer-aided machine or apparatus that has an energy sourcesuch as a laser beam to melt or sinter powder to build the structure onelayer at a time according to the model selected in the database of thecomputer component of the machine.

For example, RMT is an additive fabrication technique for manufacturingobjects by sequential delivering energy and/or material to specifiedpoints in space to produce that part. Particularly, the objects can beproduced in a layer-wise fashion from laser-fusible powders that aredispensed one layer at a time. The powder is fused, melted, remelted, orsintered, by application of the laser energy that is directed inraster-scan fashion to portions of the powder layer corresponding to across section of the object. After fusing the powder on one particularlayer, an additional layer of powder is dispensed, and the process isrepeated until the object is completed.

Detailed descriptions of selective laser sintering technology may befound in U.S. Pat. Nos. 4,863,538; 5,017,753; 5,076,869; and 4,944,817,the disclosures of which are incorporated by reference herein in theirentirety. Current practice is to control the manufacturing process bycomputer using a mathematical model created with the aid of a computer.Consequently, RMT such as selective laser re-melting and sinteringtechnologies have enabled the direct manufacture of solid or 3-Dstructures of high resolution and dimensional accuracy from a variety ofmaterials.

In one embodiment of the present invention, the porous structure isformed from powder that is selected from the group consisting of metal,ceramic, metal-ceramic (cermet), glass, glass-ceramic, polymer,composite, and combinations thereof. In another embodiment, metallicpowder is used and is selected from the group consisting of titanium,titanium alloy, zirconium, zirconium alloy, niobium, niobium alloy,tantalum, tantalum alloy, nickel-chromium, (e.g., stainless steel),cobalt-chromium alloy and combinations thereof.

As known by those skilled in the art, creating models of cells orstructures according to the disclosure of the present invention can bedone with computer aided design (CAD) software or other similarsoftware. In one embodiment, the model is built by starting with a priorart configuration and modifying the struts and nodes of the prior artconfiguration by either (1) adjusting the number struts that intersectat a node, such as the configurations in FIGS. 3-8, 11A-11F, 12A-12D,17-20 , or 22-23, or (2) introduce curved portions to the struts such asthe configurations in FIG. 13A-13M, 14, 15A-15C, 16 , or 58-61. Inanother embodiment, curved “ring-like” struts can be added to form cellillustrated in FIG. 25A-25B, 29A, 37A-37B, 38, 39A-39C, 42, 51A-51B,53A-53D, or 55A-55B. Referring to FIG. 26 , in one embodiment, thesecells can be formed by starting with a frame 2600 based on a polyhedron,such as a dodecahedron. Referring to FIG. 27 , the next step is toinscribe circles within each face of the frame 2600 to form frame 2700,which is frame 2800 superimposed on frame 2600. Subsequently, frame 2600can be removed from frame 2700, leaving only frame 2800. The thicknessand shape of the cross-section of frame 2800 can be selected to form acompleted cell, such as cell 2900 in FIG. 29A. As discussed above, aportion of the faces of frame 2600 can be inscribed with circles and/ora portion of frame 2600 can be removed to form, or frame 2600 is notremoved at all. The cells formed by such combinations are illustrated inFIGS. 37A-37B, 38, and 39A-39C. As shown by FIGS. 48-53 and 55 , thesame steps can be applied to any type of frames based on a polyhedron.Also with the aid of computer software, stacking, tiling, or repeatingalgorithm can be applied to create a model of a porous structure withthe desired dimensions formed from unit cells or struts and nodes of thepresent invention. One such stacking algorithm is space fillingtessellation shown by FIGS. 43-45 . As mentioned above, the methodsdisclosed in U.S. Application No. 61/260,811, which is incorporated byreference herein in its entirety, can be applied to stack the cells ofthe present invention or to form the struts according to the disclosuresof the present invention by controlled randomization.

Although the present invention and its advantages have been described indetail, it should be understood that various changes, substitutions, andalterations can be made herein without departing from the spirit andscope of the invention as defined by the appended claims. Moreover, thescope of the present application is not intended to be limited to theparticular embodiments of the process, machine, manufacture, compositionof matter, means, methods and steps described in the specification. Asone of ordinary skill in the art will readily appreciate from thedisclosure of the present invention, processes, machines, manufacture,compositions of matter, means, methods, or steps, presently existing orlater to be developed that perform substantially the same function orachieve substantially the same result as the corresponding embodimentsdescribed herein may be utilized according to the present invention.Accordingly, the appended claims are intended to include within theirscope such processes, machines, manufacture, compositions of matter,means, methods, or steps.

What is claimed is:
 1. A metal foam structure comprising: a plurality ofstruts, each strut comprising an elongated body portion between a firstend and a second end, wherein each strut comprises a curved bodyportion, a straight body portion, or a body portion having a combinationof curved portions and straight portions; and a plurality of nodes,wherein each node comprises a tangential intersection of a curvedportion of a first strut with a curved or straight portion of a secondstrut or an intersection of a first or second end of a first strut withthe elongated body portion of a second strut; wherein no more than twoof the struts intersect at each node.
 2. The metal foam structure ofclaim 1, wherein the metal foam structure forms a unit polyhedral cell.3. The metal foam structure of claim 2, wherein the unit polyhedral cellis a structure having between 4 and 24 sides.
 4. The metal foamstructure of claim 3, wherein the unit polyhedral cell is adodecahedron.
 5. The metal foam structure of claim 2, wherein all of theplurality of struts have curved body portions.
 6. The metal foamstructure of claim 2, wherein struts having a curved body portion formrings or ring segments which are interconnected to form open sides orfenestrations of the unit cell.
 7. The metal foam structure of claim 6,wherein one or more ring segments, alone or in combination with straightportions of struts, form a shared wall portion connecting two adjacentunit cells.
 8. The metal foam structure of claim 1, wherein the firstend of each strut has a first diameter, the second end of each strut hasa second diameter and the elongated body portion of each strut has athird diameter, wherein the first and second diameters are larger thanthe third diameter.
 9. The metal foam structure of claim 8, wherein thefirst end portion of each strut is a fluted end portion that flares fromthe third diameter to the first diameter and wherein the second endportion of each strut is a fluted end portion that flares from the thirddiameter to the second diameter.
 10. The metal foam structure of claim9, wherein the fluted first and second end portions flares outwardly inall directions from a longitudinal axis of the first or second endportions respectively.
 11. The metal foam structure of claim 10, whereinthe first and second end portions flare in a parabolic fluted shape or atapered frusto-conic shape.
 12. The metal foam structure of claim 1,further comprising: a plurality of open pores defined between thestruts.
 13. The metal foam structure of claim 12, wherein the pluralityof open pores are asymmetrical in shape.
 14. The metal foam structure ofclaim 1, wherein some or all of the struts may grow or shrink incross-sectional diameter at similar, different or identical rates alonga predetermined length of the body portion of the strut.
 15. The metalfoam structure of claim 1, wherein some or all of the struts may have avarying cross-sectional diameter that includes a minimum diameterbetween the first and second ends.
 16. The metal foam structure of claim1, wherein the metal foam structure is formed by a rapid manufacturingtechnique.
 17. The metal foam structure of claim 16, wherein the metalfoam structure is formed from a material selected from a groupconsisting of metal, ceramic, metal-ceramic (cermet), glass,glass-ceramic, polymer, composite and combinations thereof.
 18. Themetal foam structure of claim 16, wherein the metal foam structure isformed from a metallic powder selected from a group consisting oftitanium, titanium alloy, zirconium, zirconium alloy, niobium, niobiumalloy, tantalum, tantalum alloy, nickel-chromium, cobalt-chromium alloyand combinations thereof.
 19. The metal foam structure of claim 1,wherein the metal foam structure is biocompatible.
 20. The metal foamstructure of claim 19, wherein the metal foam structure is anorthopedic, dental or vascular implant.